Related papers: The fast track to L\"owner's theorem
We give canonical forms of selfadjoint and isometric operators on a complex vector space $U$ with scalar product given by a positive semidefinite Hermitian form, and of Hermitian forms on $U$. For an arbitrary system of semiunitary spaces…
We consider two operations on the Mittag-Leffler function which cancel the exponential term in the expansion at infinity, and generate a completely monotonic function. The first one is the action of a certain differential-difference…
We establish a coupled fixed points theorem for a meaningful class of mixed monotone multivalued operators and then we use it to derive some results on existence of quasisolutions and solutions to first--order functional differential…
The notion of a firmly nonexpansive mapping is central in fixed point theory because of attractive convergence properties for iterates and the correspondence with maximal monotone operators due to Minty. In this paper, we systematically…
In this paper we obtain several extension properties for monotone and sublinear operators. The results obtained generalize those known for positive and linear operators.
Our main theorem is in the generality of the axioms of Hilbert space, and the theory of unbounded operators. Consider two Hilbert spaces such that their intersection contains a fixed vector space D. It is of interest to make a precise…
We introduce a penalty term-based splitting algorithm with inertial effects designed for solving monotone inclusion problems involving the sum of maximally monotone operators and the convex normal cone to the (nonempty) set of zeros of a…
We consider positive operator valued measures whose image is the bounded operators acting on an infinite-dimensional Hilbert space, and we relax, when possible, the usual assumption of positivity of the operator valued measure seen in the…
This paper is aimed to prove a quantitative estimate (in terms of the modulus of continuity) for the convergence in the nonlinear version of Korovkin's theorem for sequences of weakly nonlinear and monotone operators defined on spaces of…
We first strictly expressed the basic notions and research methods of abstract operators, which systematically expounded the main results of abstract operator theory. By combining abstract operators with the Laplace transform, we can easily…
We introduce the notion of bilinear moment functional and study their general properties. The analogue of Favard's theorem for moment functionals is proven. The notion of semi-classical bilinear functionals is introduced as a generalization…
Any maximal monotone operator can be characterized by a convex function. The family of such convex functions is invariant under a transformation connected with the Fenchel-Legendre conjugation. We prove that there exist a convex…
The extension problem asks whether positive semi-definite functions on a symmetric unital subset of a discrete group can be extended to positive semi-definite functions on the whole group. It has been known at least since the work of Rudin…
We obtain sufficient conditions for an exponential type entire function not to have zeros in the open lower half-plane. An exact inequality containing the real and imaginary parts of such functions and their derivatives restricted to the…
Given a topological group $G$ and a unitary representation $U$ of $G$, we consider the problem of classifying the positive operator measures which are based on a $G$-homogeneous space $X$ and covariant with respect to the representation…
In [B1, Theorem 2.36] we proved the equivalence of six conditions on a continuous function f on an interval. These conditions define a subset of the set of operator convex functions, whose elements are called strongly operator convex. Two…
We introduce a suitable notion of integral operators (comprising the fractional Laplacian as a particular case) acting on functions with minimal requirements at infinity. For these functions, the classical definition would lead to divergent…
We consider the bosonic Fock space over the Hilbert space of transversal vector fields in three dimensions. This space carries a canonical representation of the group of rotations. For a certain class of operators in Fock space we show that…
The class of matrix optimization problems (MOPs) has been recognized in recent years to be a powerful tool by researchers far beyond the optimization community to model many important applications involving structured low rank matrices.…
The analytic implicit function theorem is extended. The function f of the theorem is integrated with respect to the dependent variable of the implicit function. A geometrical interpretation is given for the sub-geometry of the integral…